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If n and k are integers, is (−1)^(4n+k) less than 0?

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If n and k are integers, is (−1)^(4n+k) less than 0?  [#permalink]

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New post 29 Mar 2019, 06:01
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If n and k are integers, is (−1)^(4n+k) less than 0?

(1) n is an even number
(2) k is an odd number

C-Trap Q

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Re: If n and k are integers, is (−1)^(4n+k) less than 0?  [#permalink]

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New post 29 Mar 2019, 06:14
If n and k are integers, is (−1)^(4n+k) less than 0?

\((−1)^{(4n+k)}=(-1)^{4n}*(-1)^k=((-1)^2)^{2n}+(-1)^1*(-1)^k\)
So we require to know the property of k.
If it is odd, \((−1)^{(4n+k)}<0\), and if k is even, \((−1)^{(4n+k)}>0\)

(1) n is an even number
We require the property of k.

(2) k is an odd number
So, answer is YES for 'Is (−1)^(4n+k) less than 0?
Sufficient

B'
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If n and k are integers, is (−1)^(4n+k) less than 0?  [#permalink]

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New post Updated on: 29 Mar 2019, 08:17
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dabaobao wrote:
If n and k are integers, is (−1)^(4n+k) less than 0?

(1) n is an even number
(2) k is an odd number

C-Trap Q


C-Trap Q



Theory:


(-1)^even power = always +
(-1)^odd power = always -

Simplify the Q


4n is always even. So (-1)^4n would always be +
So we only care about (-1)^k. If we know the power of k, then we can tell whether (−1)^(4n+k) is <0 or >0.

Hence, simplified Q: Is k even or odd?

Solving the Simplified Q



1) Don't care about whether n is even or odd since 4n would always be even. Hence (−1)^(4n) would be even. Need k. Not sufficient.

2) K=odd. This is what we wanted sufficient.

Make sure to not fall in the C-Trap by thinking that you need both k and n. This is a common trap that GMAT likes to use on 700 level Qs.

Hence, answer = B.
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Originally posted by dabaobao on 29 Mar 2019, 06:19.
Last edited by dabaobao on 29 Mar 2019, 08:17, edited 1 time in total.
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If n and k are integers, is (−1)^(4n+k) less than 0?  [#permalink]

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New post 29 Mar 2019, 06:50
First of all, rewrite the given number as: \(-1^{4n} * -1^k\).
Statement 1: we don't know anything about \(k\). If \(k\) was even, the number would be positive; otherwise, if \(k\) was odd, the number would be negative. Provided information is not sufficient.
Statement 2: \(k\) is odd. Since \(4n = even * odd/even = even\), what we derive is \(-1^{4n} = positive\) and \(-1^k = negative\). The whole number will be less than \(0\). Sufficient. Hence, B.
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Re: If n and k are integers, is (−1)^(4n+k) less than 0?  [#permalink]

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New post 29 Mar 2019, 11:10
dabaobao wrote:
If n and k are integers, is (−1)^(4n+k) less than 0?

(1) n is an even number
(2) k is an odd number

C-Trap Q


#1
value of k not know
#2
odd = k and 4n= even
so value <0
IMO B
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Re: If n and k are integers, is (−1)^(4n+k) less than 0?   [#permalink] 29 Mar 2019, 11:10
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